Objectives. Current approaches via physiological features detecting aberrant driving behaviour (ADB), including speeding, abrupt steering, hard braking and aggressive acceleration, are developing. This study proposes using machine learning approaches incorporating heart rate variability (HRV) parameters to predict ADB occurrence. Methods. Naturalistic driving data of 10 highway bus drivers in Taiwan from their daily routes were collected for 4 consecutive days. Their driving behaviours and physiological data during a driving task were determined using a navigation mobile application and heart rate watch. Participants\' self-reported data on sleep, driving-related experience, open-source data on weather and the traffic congestion level were obtained. Five machine learning models - logistic regression, random forest, naive Bayes, support vector machine and gated recurrent unit (GRU) - were employed to predict ADBs. Results. Most drivers with ADB had low sleep efficiency (</=80%), with significantly higher scores in driver behaviour questionnaire subcategories of lapses and errors and in the Karolinska sleepiness scale than those without ADBs. Moreover, HRV parameters were significantly different between baseline and pre-ADB event measurements. GRU had the highest accuracy (81.16-84.22%). Conclusions. Sleep deficit may be related to the increased fatigue level and ADB occurrence predicted from HRV-based models among bus drivers.